The cost to produce one compact disc is $
1.75 plus a one-time fixed cost of $
2400. The revenue received from selling one compact disc is $
12.
(c) Profit equals revenue minus cost. Write a formula that calculates the profit P from selling x compact discs.
P=
enter your response here (Simplify your answer.)
P = (12x) - (1.75x + 2400)
The cost to produce one compact disc is $
1.75 plus a one-time fixed cost of $
2400. The revenue received from selling one compact disc is $
12.
Question content area bottom
Part 1
(a) Write a formula that gives the cost C of producing x compact discs. Be sure to include the fixed cost.
C
=
1.75 x plus 2400
1.75x+2400 (Simplify your answer.)
Part 2
(b) Write a formula that gives the revenue R from selling x compact discs.
R
=
12 x
12x (Simplify your answer.)
Part 3
(c) Profit equals revenue minus cost. Write a formula that calculates the profit P from selling x compact discs.
P
=
10.25 x minus 2400
10.25x−2400 (Simplify your answer.)
Part 4
(d) How many compact discs need to be sold to yield a positive profit?
enter your response here
or more compact discs should be sold.
(Simplify your answer.)
Part 4:
To yield a positive profit, the formula for profit (P) should be greater than zero:
10.25x - 2400 > 0
Solving this inequality, we have:
10.25x > 2400
x > 2400/10.25
x > 234.15
Therefore, more than 234 compact discs should be sold to yield a positive profit.
The cost to produce one compact disc is $
1.75 plus a one-time fixed cost of $
2400. The revenue received from selling one compact disc is $
12.
(d) How many compact discs need to be sold to yield a positive profit?
enter your response here
or more compact discs should be sold.
(Simplify your answer.)
To calculate the number of compact discs that need to be sold to yield a positive profit, we can set the profit equation (P) to be greater than zero:
P > 0
Substituting the given values, the profit equation is:
(12x) - (1.75x + 2400) > 0
Simplifying the equation:
12x - 1.75x - 2400 > 0
10.25x - 2400 > 0
To solve for x, we isolate the variable:
10.25x > 2400
x > 2400/10.25
x > 234.15
Therefore, more than 234 compact discs need to be sold to yield a positive profit.
To calculate the profit, we subtract the cost from the revenue. The cost to produce one compact disc is $1.75 plus a one-time fixed cost of $2400. The revenue received from selling one compact disc is $12.
Let's break down the formula step by step:
- The cost for producing x compact discs would be (1.75 * x) + 2400, as the variable cost ($1.75) is multiplied by x (the number of compact discs) and added to the fixed cost ($2400).
- The revenue from selling x compact discs would be 12 * x, as the revenue of $12 per compact disc is multiplied by x (the number of compact discs).
- To calculate the profit (P) from selling x compact discs, we subtract the cost formula from the revenue formula:
P = (12 * x) - ((1.75 * x) + 2400)
Simplifying this equation, we can combine like terms:
P = 12x - 1.75x - 2400
Further simplification gives:
P = 10.25x - 2400
Therefore, the formula that calculates the profit (P) from selling x compact discs is:
P = 10.25x - 2400